The harmonic nodes are at certain disivions of the string, e.g. 1:2, 1:3 etc.

So the positions always stay the same, as do the pitches <b>relative</b> to the pitch of the open string and to each other.
They change of course in abolute pitch as you change the pitch of the open string.

All this of course refers to a single string, on alternate tunings the patterns that stretch over several strings change when you tune the strings in other intervals than the standard 4ths.